If `sin^-1 (x/a) +sin^-1 (y/b) = sin^-1 (c^2/(ab))` then prove that `b^2x^2 +2xysqrt(a^2b^2-c^2) = c^4-a^2y^2-2x^2y^2`

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-y^2) + y sqrt(1-x^2) =1 .

If x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3)) , then prove that y^2 = 1 - x

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that x^(2)-y^(2)+z^(2)-2xz sqrt(1-y^(2))=0

If cos ^(-1) .(x)/(a)+ cos ^(-1). (y)/(b) = theta then prove that (x^(2))/(a^(2)) -(2xy)/(ab) . cos theta+ (y^(2))/(b^(2)) = sin ^(2) theta .

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2x y z

If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y^3)

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha